Laurence,
The second function is not too difficult.
f[n_?OddQ] := 1/n
f[n_?EvenQ] := n
tab = Table[f[n], {n, 1, 20}]
{1, 2, 1/3, 4, 1/5, 6, 1/7, 8, 1/9, 10, 1/11, 12, 1/13, 14, 1/15, 16, 1/17,
18,1/19, 20}
We could plot the results using Log for a more balanced picture.
ListPlot[Log[tab], Prolog -> AbsolutePointSize[4]];
For non-integers the function is undefined and we just get the input back.
f[3.5]
f[3.5]
But I don't think there is a similar solution within Mathematica for your
first case . The problem is how can you feed a general irrational value to
Mathematica in a way that Mathematica can know it is irrational. Something
like the following doesn't work.
g[x_Rational | x_Integer] := x
g[x_Real] := 1/x
g[2]
2
But
g[2.0]
0.5
does not treat 2.0 as rational. Maybe you will get a better answer on this
part.
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: lorenzo.keegan at handbag.com [mailto:lorenzo.keegan at handbag.com]
To: mathgroup at smc.vnet.net
Hello,
Can you help me?
How do write expressions in Mathematica for functions and sequences
such as the following:
f(x) = {1/x, x is irrational
{x^2, x rational
and
f(n) = 1/n, n odd
n^2, n even
I am a new user and find the manual rather daunting.
Best wishes
Laurence Keegan